Least Common Multiple (LCM) of 97 and 102
The least common multiple (LCM) of 97 and 102 is 9894.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 97 and 102?
First, calculate the GCD of 97 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 102 = 0 remainder 97 |
| 2 | 102 ÷ 97 = 1 remainder 5 |
| 3 | 97 ÷ 5 = 19 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 157 | 7693 |
| 132 and 17 | 2244 |
| 54 and 92 | 2484 |
| 25 and 31 | 775 |
| 48 and 45 | 720 |